FOCK SPACE REALIZATIONS OF SOME CLASSICAL MARKOV
PROCESSES
Włodzimierz Bryc
Wiktor Ejsmont
Abstract: We define a pair of non-commutative processes on a perturbed Fock space. Both
processes have the same univariate distributions and satisfy a weak form of the polynomial
martingale property. The processes give two non-equivalent Fock-space realizations of the
same classical Markov process: the two-parameter bi-Poisson processes introduced in [12],
and constructed in [13].
2000 AMS Mathematics Subject Classification: Primary: 46L54; Secondary:
46L53.
Keywords and phrases: Markov processes, non-commutative probability, bi-Poisson
processes.